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David MUKAMEL (Weizmann Institute)5/31/23, 10:15 AM
The long-range nature of the effect of a pump or a battery on an interacting diffusive fluid is discussed. It is shown that off criticality the pump generates long-range modulation in the density profile of the form of a dipolar electric potential and a current profile in the form of a dipolar electric field. The density profile is drastically modified when the fluid is at its critical point:...
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Stefano OLLA (Dauphine)5/31/23, 11:30 AM
We investigate the macroscopic behaviour of the density fluctuations of a one dimensional dynamics of hard rods with random length. After recentering on the effective velocity the density fluctuations of particles of a given velocity v on the diffusive space-time scaling will evolve driven by a browian motion with a diffusivity depending on v. This rigid evolution of fluctuations is expected...
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Bernard DERRIDA (Collége de France)5/31/23, 12:15 PM
The shift of the position of a front found by Bramson in the case of the Fisher-KPP equation is modified at the transition between pulled and pushed fronts. Based on an exactly solvable case, one can predict the cross-over function which determines this shift near this transition. The correction due to a cut-off is also modified at this transition. This raises the question of whether the...
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Marielle SIMON (ENS-Lyon)5/31/23, 2:15 PM
In this talk we will be interested in a one-dimensional exclusion process subject to strong kinetic constraints, which belongs to the class of cooperative kinetically constrained lattice gases. More precisely, its stochastic short range interaction exhibits a continuous phase transition to an absorbing state at a critical value of the particle density. In one dimension, and if the microscopic...
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Tomohiro SASAMOTO (TokyoTech)5/31/23, 3:00 PM
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Davide GABRIELLI (DISIM, La Aquila)5/31/23, 4:15 PM
Stationary non equilibrium states (SNS) have a rich and complex structure. The large deviations rate functionals for the empirical measure of a few one dimensional SNS of stochastic interacting systems have been computed, among wich the exclusion process and the Kipnis-Marchioro-Presutti (KMP) model. The corresponding rate functionals are not local due to the presence of long range...
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Denis BERNARD (ENS Paris)5/31/23, 5:00 PM
An alternative title could have been “How to characterise fluctuations in diffusive out-of-equilibrium many-body quantum systems?” In general, the difficulty to characterise non-equilibrium systems lies in the fact that there is no analog of the Boltzmann distribution to describe thermodynamic variables and their fluctuations. Over the last 20 years, however, it was observed that fluctuations...
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Ivan LOBASKIN (Edinburgh University)5/31/23, 5:45 PM
Single-file diffusion with a defect particle is fundamental to the understanding of driven tracers in narrow channels. In this talk, two variations on the simple exclusion process on a ring geometry are considered as minimal models of such a setup. The first variation is a totally asymmetric tracer in a bath of symmetric particles. The second variation is a defect particle with priority in a...
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Thierry BODINEAU (IHES)6/1/23, 9:30 AM
For finite size Markov chains, the Donsker-Varadhan theory fully describes the large deviations of the time averaged empirical measure. In this talk, we consider the large size asymptotics of the Donsker-Varadhan functional associated with the one-dimensional symmetric simple exclusion process connected with reservoirs at different densities. The Donsker-Varadhan functional encodes a variety...
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Olivier BÉNICHOU (Sorbonne Université)6/1/23, 10:15 AM
Single-file transport, where particles diffuse in narrow channels while not overtaking each other, is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous behavior originates from strong bath-tracer correlations in 1D, which have however remained elusive, because they involve an infinite hierarchy of equations....
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Percy DEIFT (Courant Institute, NYU)6/1/23, 11:30 AM
We describe an approach to the Toda lattice relying only on basis facts of linear algebra, making no use of symplectic geometry. This approach is due to Leite et al, and has many advantages, particularly to the analysis of the long-time behavior of solutions of the Toda lattice.
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Herbert SPOHN (TUM Munich University)6/1/23, 12:15 PM
Integrable many-particle systems arise in wide variety. To illustrate their generalized hydrodynamics, the Calogero fluid will be used as prime example. The fluid consists of classical particles moving on the line and interacting through the repulsive 1/sinh^2 pair potential. Discussed are generalized Gibbs ensembles, the corresponding random Lax matrix, its density of states, and GGE averaged...
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Jorge KURCHAN (ENS Paris)6/1/23, 2:15 PM
A family of transport models, including the better understood ones, may be mapped onto a dual model that is simpler,
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or directly to an equilibrium problem. These properties, unrelated to integrability, are easily understood once one uncovers the group structure
behind them. This structure also allows one to extend the constructions to the quantum case, with minimal mental effort. -
Makiko SADADA (Tokyo University)6/1/23, 3:00 PM
Over the past 30 years, the hydrodynamic limit has been proved for many interacting particle systems. However, there are still many models for which rigorous proofs are missing, especially those called non-gradient models. Also, most of the existing results are for models on Z^d lattices with one conserved quantity. There has been no theory of how much existing theories can be generalized, and...
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Joel LEBOWITZ (Rutgers)6/1/23, 4:15 PM
We consider a translation invariant point process in R^d or Z^d. Let
V(N_B) be the variance in the number of points, N_B, in a ball B of
volume |B|. Generally, such as when particles with short range interactions are
distributed according to a Gibbs measure, V(N_B)/|B| >0.There are however many interesting cases when Var(N_B)/N_B->0, as
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|B|->oo. Such processes are called hyperuniform... -
Hiroki MORIYA (LPTMC)6/1/23, 5:00 PM
Over the last two decades, the macroscopic fluctuation theory has been developed and applied to various diffusive models to study large-scale fluctuations of physical quantities such as current. The equations of motion that the theory induces are in general quite difficult to solve under the appropriate mixed time boundary conditions. Fortunately, as long as the equations of motion belong to a...
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Benjamin DOYON (King's College)6/2/23, 9:30 AM
Evaluating fluctuations and correlations at large scales of space and time in quantum and classical many-body systems, in and out of equilibrium, is one of the most important problems of emergent physics. I will explain how basic hydrodynamic principles give access to exact results at the ballistic scale, solely from the data of the Euler-scale hydrodynamic equations of the many-body system....
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Patricia GONÇALVES (IST, Lisbon University)6/2/23, 10:15 AM
In this talk, I will present a model which was introduced in [1] and
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consists of an exclusion process with different types of particles,
let us say types A, B, and C. Depending on the interaction rate
between different types of particles, the limiting fluctuations end up
in different universality classes: either the fluctuations are
governed by energy solutions of the stochastic Burgers... -
Gianni JONA-LASINIO (La Sapienza, Rome)6/2/23, 11:30 AM
The macroscopic fluctuation theory (MFT) is a consistent and self-contained description of macroscopic fluctuations using
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only transport coefficients. In the formulation of the Rome group an important motivation was the discovery that we could reproduce by a purely macroscopic calculation the result of Derrida, Lebowitz and Speer obtained solving the microscopic symmetric simple exclusion... -
Pierre LE DOUSSAL (ENS Paris)6/2/23, 12:15 PM
The large deviations for the diffusion of a tracer in a 1D time dependent medium can be described, on diffusive scales,
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by the macroscopic fluctuation theory (MFT).
The corresponding MFT variational equations are mapped to the integrable derivative non-linear Schrodinger
equation. We provide a solution using inverse scattering methods, and obtain the large deviation rate function
for the... -
Satya MAJUMDAR (LPTMS-Saclay)6/2/23, 2:15 PM
For any stochastic time-series of duration T, the time t_max at which
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the process achieves its maximum is an important observable. For example,
for a stock price over a trading period T, one would like to sell the
stock at the time when the price is maximal. I'll discuss the statistics
of t_max for a variety of stochastic processes. In particular, for a large class
of stationary... -
Julien BARRÉ (Institut Poisson, Université d'Orléans)6/2/23, 3:00 PM
To derive a macroscopic description of a system (in terms of
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hydrodynamical fields), starting from a microscopic one (in terms of
interacting particles), the usual route introduces an intermediate
kinetic equation, and takes advantage of the difference of time scales
between fast and slow modes to set up a Chapman-Enskog expansion. When
finite size effects are important at the macroscopic... -
Baruch MEERSON (Hebrew University, Jerusalem)6/2/23, 3:45 PM
The “Brownian bees” model, suggested by J. Berestycki, E. Brunet, J. Nolen, and S. Penington, is a new member of a family of Brunet-Derrida particle systems which mimic some aspects of biological selection. Like other Brunet-Derrida systems, the Brownian bees can be also considered as a system of interacting particles with reset. The model describes an ensemble of N independent branching...
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